Internal problem ID [11636]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime }=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve((x^3+y(x)^2*sqrt(x^2+y(x)^2))-x*y(x)*sqrt(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {\left (y \left (x \right )^{2}+x^{2}\right )^{\frac {3}{2}}}{x^{3}}+3 \ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 28.664 (sec). Leaf size: 265
DSolve[(x^3+y[x]^2*Sqrt[x^2+y[x]^2])-x*y[x]*Sqrt[x^2+y[x]^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-\frac {1}{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) \sqrt [3]{x^6 (\log (x)+c_1){}^2}} y(x)\to \sqrt {-x^2-\frac {1}{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) \sqrt [3]{x^6 (\log (x)+c_1){}^2}} y(x)\to -\sqrt {-x^2-\frac {1}{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) \sqrt [3]{x^6 (\log (x)+c_1){}^2}} y(x)\to \sqrt {-x^2-\frac {1}{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) \sqrt [3]{x^6 (\log (x)+c_1){}^2}} y(x)\to -\sqrt {-x^2+3^{2/3} \sqrt [3]{x^6 (\log (x)+c_1){}^2}} y(x)\to \sqrt {-x^2+3^{2/3} \sqrt [3]{x^6 (\log (x)+c_1){}^2}} \end{align*}